# End to end learning and optimization on graphs

arXiv: https://arxiv.org/abs/1905.13732 · HTML: https://mlsanity.com/paper/1905.13732/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2019.

## Built on by (most cited first, 30 of 44)

- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [On Training Implicit Models](https://mlsanity.com/paper/2111.05177/) (2021)
- [CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints](https://mlsanity.com/paper/2105.02343/) (2021)
- [Integrated Conditional Estimation-Optimization](https://mlsanity.com/paper/2110.12351/) (2021)
- [SurCo: Learning Linear Surrogates For Combinatorial Nonlinear Optimization Problems](https://mlsanity.com/paper/2210.12547/) (2022)
- [Estimate-Then-Optimize versus Integrated-Estimation-Optimization versus Sample Average Approximation: A Stochastic Dominance Perspective](https://mlsanity.com/paper/2304.06833/) (2023)
- [Leaving the Nest: Going Beyond Local Loss Functions for Predict-Then-Optimize](https://mlsanity.com/paper/2305.16830/) (2023)
- [Landscape Surrogate: Learning Decision Losses for Mathematical Optimization Under Partial Information](https://mlsanity.com/paper/2307.08964/) (2023)
- [The Perils of Learning Before Optimizing](https://mlsanity.com/paper/2106.10349/) (2021)
- [A Survey on Influence Maximization: From an ML-Based Combinatorial Optimization](https://mlsanity.com/paper/2211.03074/) (2022)
- [Decision-Focused Learning without Differentiable Optimization: Learning Locally Optimized Decision Losses](https://mlsanity.com/paper/2203.16067/) (2022)
- [Combinatorial Optimization for Panoptic Segmentation: A Fully Differentiable Approach](https://mlsanity.com/paper/2106.03188/) (2021)
- [Partition and Code: learning how to compress graphs](https://mlsanity.com/paper/2107.01952/) (2021)
- [LPGD: A General Framework for Backpropagation through Embedded Optimization Layers](https://mlsanity.com/paper/2407.05920/) (2024)
- [Global-Decision-Focused Neural ODEs for Proactive Grid Resilience Management](https://mlsanity.com/paper/2502.18321/) (2025)
- [Link Prediction without Graph Neural Networks](https://mlsanity.com/paper/2305.13656/) (2023)
- [Contrastive Representation Learning Based on Multiple Node-centered Subgraphs](https://mlsanity.com/paper/2308.16441/) (2023)
- [GenCO: Generating Diverse Designs with Combinatorial Constraints](https://mlsanity.com/paper/2310.02442/) (2023)
- [End-to-End Analysis of Charge Stability Diagrams with Transformers](https://mlsanity.com/paper/2508.15710/) (2025)
- [Combinatorial Optimization Augmented Machine Learning](https://mlsanity.com/paper/2601.10583/) (2026)
- [Policy-Embedded Graph Expansion: Networked HIV Testing with Diffusion-Driven Network Samples](https://mlsanity.com/paper/2601.16233/) (2026)
- [Memory-Augmented Graph Neural Networks: A Brain-Inspired Review](https://mlsanity.com/paper/2209.10818/) (2022)
- [Self-supervised Equality Embedded Deep Lagrange Dual for Approximate Constrained Optimization](https://mlsanity.com/paper/2306.06674/) (2023)
- [Fully Linear Graph Convolutional Networks for Semi-Supervised Learning and Clustering](https://mlsanity.com/paper/2111.07942/) (2021)
- [Beyond NaN: Resiliency of Optimization Layers in The Face of Infeasibility](https://mlsanity.com/paper/2202.06242/) (2022)
- [Decision-Focused Model-based Reinforcement Learning for Reward Transfer](https://mlsanity.com/paper/2304.03365/) (2023)
- [Attribute-Enhanced Similarity Ranking for Sparse Link Prediction](https://mlsanity.com/paper/2412.00261/) (2024)
- [DistrictNet: Decision-aware learning for geographical districting](https://mlsanity.com/paper/2412.08287/) (2024)

## Abstract (arXiv)

Real-world applications often combine learning and optimization problems on graphs. For instance, our objective may be to cluster the graph in order to detect meaningful communities (or solve other common graph optimization problems such as facility location, maxcut, and so on). However, graphs or related attributes are often only partially observed, introducing learning problems such as link prediction which must be solved prior to optimization. Standard approaches treat learning and optimization entirely separately, while recent machine learning work aims to predict the optimal solution directly from the inputs. Here, we propose an alternative decision-focused learning approach that integrates a differentiable proxy for common graph optimization problems as a layer in learned systems. The main idea is to learn a representation that maps the original optimization problem onto a simpler proxy problem that can be efficiently differentiated through. Experimental results show that our ClusterNet system outperforms both pure end-to-end approaches (that directly predict the optimal solution) and standard approaches that entirely separate learning and optimization. Code for our system is available at https://github.com/bwilder0/clusternet.